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The leading actor-producer-director wrote on his blog that box office takings for the coming-of-age comedy had already surpassed those for his 2008 hit Ghajini, which was the previous record holder.
"In less than 10 days 3i has overtaken the entire business of Ghajin, India, Overseas, everywhere!!! And is still going strong," Khan wrote on Monday, describing himself as "fully overwhelmed and totally humbled."
India's Business Standard newspaper said on Tuesday that 3 Idiots had taken 2.4 billion rupees ($51 million) from the domestic and international market since opening on December 25. Ghajini took 2.25 billion rupees.
Meanwhile www.hollywood.com and Deadline Hollywood, which both track box office takings in the United States, said 3 Idiots has so far made $4.8 million after opening in nearly 120 US theatres.
No Bollywood film has crossed the $4 million threshold before.
The film's success has given Bollywood a boost, after a disappointing 2009 marked by a damaging producers' boycott of multiplex cinemas in a row over box office takings, swine flu fears and a string of big budget flops.
The Business Standard said 3 Idiots has so far made more money than Bollywood's entire ticket receipts in November, which included the hit Ajab Prem Ki Gazab Kahani (An Amazing Story Of Strange Love).
Indian box office takings are lower than in Hollywood because of lower ticket prices.
Film critics and industry analysts attributed the success of 3 Idiots not just to Khan's star quality, but also high production values, a sustained marketing campaign and the story's wide appeal.
A public row about how much the film was based on Chetan Bhagat's best-seller Five Point Someone, and a lack of other big-name releases, may also have helped.
"It's a very well-made film with a message and with a big star. It brings back memories of people's experience of the education system in India," Taran Adarsh, from bollywoodhungama.com, said of the film's overseas success.
"If you still have family here I think you identify with it all the more," he said.
Mayank Shekhar, national cultural editor at The Hindustan Times newspaper, said the same expatriate Indian "IT crowd" who bought Five Point Someone appear to have flocked to US cinemas, boosting audiences.
"What's equally important is that it's not a preachy film. It's by itself a complete comedy, which is what most mainstream audiences go for," he said.
A well-constructed combination of a leading star, well-placed song-and-dance routines and a message gave it "all the elements of a Bollywood blockbuster," he added.
US film studios have been eyeing India's popular Hindi-language film industry for several years, hoping to tap in to an expanding $2.3 billion market.
Hopes are high that Shahrukh Khan's upcoming film My Name Is Khan will match or even eclipse the success of 3 Idiots.
Fox Searchlight, which promoted the Oscar-winning film Slumdog Millionaire, and other Fox units are handling distribution.
Adarsh said the overseas market is becoming increasingly important for Bollywood.
"The domestic market has traditionally been measured in rupees. Today it's dollars, pounds, dirham, euros and various other currencies," he said.
"It's not just the Indian diaspora. It's people in Pakistan, Bangladesh, the Middle East. The success of 3 Idiots is just the tip of the iceberg."
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